Assuming a +5 strength modifier and 10 feet of movement prior, can you jump over a medium sized creature to land on the other side?
Yes, in most cases
Half-orc 4'10" +2d10
Page 121 of the PHB
Half-orcs being the tallest medium creature in the PHB and their tallest they can get to is 6'6".
When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In som e circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can. Page 182 of the PHB
Assuming a +5 str we would calculate 3'+5'=8' which is greater than the 6'6" of our half-orc.
Therefore unless your medium creature is a lot taller than usual then there shouldn't be a problem.
Yes, when looking creature size; but not the space a creature controls
Performing a running high jump (like in the olympics...but maybe without the fosbury flop) would let you attempt to do this and that lets you (PHB, 182):
When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In som e circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.
As long as the creature is 8' or less, you can jump over them. But you may risk an Opportunity Attack.
With a strength modifier of 5, you can high jump 8'. In order to clear the controlled space of a Medium creature (5'), you need to be 10' away. Unless your DM allows you to make a strength check, you may be out of luck. The DC would likely be set keeping in mind the actual height of the creature.
If you CAN jump 10'
In order to 'clear' a medium creature that commands a 5' space, you need to:
- Run 10' to let you add your strength modifier
- Begin your Jump 5' before the target and land 5' after. Total of 10' of movement.
- Jump 10' above the target.
This sums to 30' of movement. Most creatures have this as their Movement.
*Dwarfs who have magic items like the Boots of Speed can do this
In order to jump over a medium-sized creature without it getting an opportunity attack, you will have to be able to high jump about 12' for a medium opponent with a normal weapon (more for a bugbear, or if it has a reach weapon). With a 10' running start, you can high jump 3'+your Str bonus, so that would still require a Strength bonus of +9, meaning a strength of 28. Long jump limit, again with a 10' run up, would have to be a bit more than 15', which is relatively easy with a decent strength, since the long jump distance is the same as your Str score. So height is the limiting factor, and to simply jump over (with a 10' run up) would basically require Storm Giant Strength. Maybe a bit less if the opponent is on the short side, but still, for a normal character with a max strength of 20, the high jump limit is 8', which most medium opponents could reach and thus make an opportunity attack as you went over/past. A small opponent you could probably clear with a 20 strength.
With a Jump spell, it is easy -- you'd need to jump up 4', tripled by the spell, which would require only a Str bonus of +1, or a 12 strength. In this case, the long jump is g0ing to be limited by your movement rather than your strength. With a 10' run up and a normal 30' movement, you will be able to jump 20' long (as long as you have at least a 7 strength), which is enough. If you Dash as your action, that presents more options.
Not without a house rule. High Jump mechanics only allow a character to move along the vertical axis. There are no rules providing for combining two jumps in a single movement or "walking" in a horizontal direction while high-jumping (depending on how you want to characterize it).
Long Jump (expanded answer)
@V2Blast reproduced the text of the long jump below. I suppose it could be construed as enabling a jump over an enemy--so long as a long jump's distance is at least four times the enemy's height. Given that a bipedal creature in the medium size category normally stands somewhere between 4-8 feet, a long jump covering 16-32 feet would be necessary to clear the head of such an enemy. That does seem possible, but perhaps not without significant magical assistance or some otherwise extraordinary character feature (Monk's Step of the Wind?). You'd also probably need a luxuriously spacious tactical map to allow for that much unimpeded horizontal movement in one direction.
Finally, the above may have the absurd side effect of being able to jump higher with a long jump than with a high jump.
Yes.. but I would give them an attack of opportunity on you while you were doing so... unless you had some kind of shield skill + athletics to know how to position your shield between you and them in acrobatic fashion.
Just a brute-strength jump can get you over an enemy, but you may be flying through the air with your mid-section and vitals exposed. Enemy just pokes their sword / spear upwards and guts you.
Now, the bigger issue I see going on is that you're micro-managing combat too much. The whole point of role-playing is to abstract combat to make it flow, and then just story-tell / RP the end result of a couple of dice rolls... not micro-manage every move and then dream up all the extra rules that need to go with it to make it work. That just creates arguments and rules-lawyering.
Because if you have enough strength to jump over an enemy, why not just argue for bashing them aside to get behind them, or argue that a thief has enough dexterity to slide between their legs to get behind them.
The to-hit and damage rolls are supposed to abstract and handle all of this minutiae, that way players won't dream up crazy stuff then argue with the GM over the rules for it.
EG (good): roll to-hit.. you hit.. roll damage.. massive damage... story-tell how it happened... "you somersault over the orc, landing behind him and stabbing your sword behind you with one graceful blow... felling the opponent."
(player) I want to jump over the enemy to try to get an attack of opportunity on him (gm) Um.. ok.. I guess that would require you to roll a ... (player) My strength has a +5 modifer (gm) I was thinking more of a dex feat (player) But I want to use strength, because it requires strength to jump (gm) But it requires dexterity to somersault and land without twisting your ankle
(arguement continues, because you're trying to shoe-horn rules to fit an action, instead of dreaming up action that fits the post-rolled dice rolls that already account for both rules and abstraction of complex combat possibilities).